Analytical Results on Generating Phase-Equivalent Potentials by Supersymmetry: Removal and Addition of Bound States

Abstract

Applying the techniques of supersymmetric quantum mechanics we determine closed algebraic expressions for potentials that are phase-equivalent with the generalized Pöschl—Teller potential. Among the examples we discuss the elimination of any single bound state, adding a single bound state at specific energies and eliminating the first few bound states. In our work we applied the abstract mathematical formalism developed recently for the modification of the spectrum of potentials without changing the phase shifts, and adapted it to the case of the generalized Pöschl—Teller potential. We discuss the importance of shape invariance in these procedures and comment on the possibility of deriving similar closed formulas for various other potentials.